[雙語翻譯]橋梁工程外文翻譯--橋梁橡膠支座在受壓時(shí)的定向剪切效應(yīng)（英文）

1、Directional Effects of Shear Combined with Compression on Bridge Elastomeric BearingsHieu H. Nguyen1 and John L. Tassoulas, M.ASCE2Abstract: Elastomeric bearings are widely used in bridge supports to accommodate thermal

2、and other movements. The study presentedin this paper extends an earlier investigation of two-dimensional bearing performance to three dimensions. Large-deformation rubberhyperelasticity is reviewed and a theoretical mod

3、el is described with the steel-reinforced bearing subjected to compression in the directionthrough the thickness followed by shear in various lateral directions, including bridge longitudinal and transverse directions. C

4、omputa-tions are carried out using the general-purpose, finite-element analysis computer program, ABAQUS. Conclusions are drawn regarding theeffects of shear direction on bearing behavior.DOI: 10.1061/?ASCE?BE.1943-5592.

5、0000034CE Database subject headings: Bridges; Elastomer; Shear; Compression; Finite element method.Author keywords: Bridges; Elastomeric; Bearing; Shear; Compression; Direction; Finite element.IntroductionIn bridges, mov

6、ements and rotations of girders may occur due to temperature changes, moving loads, earthquakes, concrete shrink- age, and creep. Bearings are introduced between the girders and the piers ?or abutments? to accommodate th

7、ese movements. In elastomeric bearings ?Long 1974?, movements and rotations are accommodated by compressing or shearing layers of the rubber- like materials ?elastomers?. Elastomers can deform very substan- tially withou

8、t damage. They are typically flexible under shear and uniaxial stress but they are very stiff against volume changes ?incompressibility?. This feature makes the design of an elasto- meric bridge bearing that is stiff in

9、compression but flexible in shear possible. If the elastomer is laminated with steel shims, as shown in Fig. 1, the lateral expansion is prevented at the inter- faces and compressive deformations must be accommodated onl

10、y by bulging allowed between steel shims or between steel shims and the bridge girder or pier. A rubber pad ?plain or laminated? in contact with two rigid surfaces is the most common representation of an elastomeric bear

11、ing. The contact conditions can be fixed-fixed ?the rubber block is bonded to the two rigid surfaces?, friction-friction ?the top and bottom surfaces of the block are in frictional contact with rigid plates?, and the com

12、bination between the two, fixed-friction. Elastomeric bearings can be analyzed using approximate analyti- cal or numerical techniques. Early research by Gent, Lindley, Conversy, Meinecke, and Holownia explored approximat

13、e ana-lytical solutions for rubber blocks ?Gent and Lindley 1959; Conversy 1967; Gent and Meinecke 1970; Holownia 1971?. Gent and Lindley ?1959? showed that the compression modulus of bonded rubber blocks under compressi

14、on is a function of Young’s modulus and the shape factor, defined as the ratio of the cross- sectional area to the force-free area. In the derivation, the rubber was assumed to be a linear elastic compressible material a

15、nd the total displacements of the rubber arose from the superposition of two simple deformations: a pure homogenous deformation of the unbonded block and a subsequent lateral deformation necessary to bring the end sectio

16、ns back to the bonded condition. Gent and Meinecke ?1970?, by a similar approach, arrived at an approxi- mate theoretical treatment of bonded rubber blocks subjected to low levels of compression. The solution was extende

17、d to bending and shear of rectangular and elliptical cross-sectional rubber blocks. Also, the shear stresses at the bonded surfaces under com- pression, extension, and bending were evaluated. Later, Stanton and Roeder ?1

18、982, 1992?, Roeder et al. ?1987, 1989?, and Roeder and Stanton ?1991? reported results of combined analytical and experimental studies that led to improved design recommenda- tions. Herrmann et al. ?1988a,b? carried out

19、nonlinear finite- element analysis of elastomeric bridge bearings by means of a homogenized continuum model. Yeoh et al. ?2002? extended the investigation of two-dimensional bonded rubber block perfor- mance to three dim

20、ensions. Several shapes of rubber blocks were considered, including long strip, cylindrical disk, rectangular block, and annular block. The usual “incompressibility” assump- tion was modified to “near incompressibility”

21、toward more accu- rate solutions. More recently, Horton et al. ?2002? studied axially loaded bonded rubber blocks of long thin rectangular and circular cross sections. They derived closed-form expressions for the total a

22、xial deflection and stress distribution, which satisfy exactly the governing equations and conditions based upon the classical theory of elasticity, using a superposition approach. Fewer studies have examined rubber bloc

23、ks in the friction-friction condition. It is reasonable to expect that the compression modulus in the fric- tional contact condition is lower than in the bonded condition, as slip occurs on contact between the rubber and

24、 rigid surfaces. Ef- fectively, the compression modulus is related to the magnitude of1Graduate Student, Dept. of Civil, Architectural, and Environmental Engineering, Univ. of Texas, Austin, TX 78712. 2Professor, Dept. o

25、f Civil, Architectural, and Environmental Engineer- ing, Univ. of Texas, Austin, TX 78728 ?corresponding author?. E-mail: yannis@mail.utexas.edu Note. This manuscript was submitted on September 12, 2008; ap- proved on Fe

26、bruary 24, 2009; published online on April 13, 2009. Dis- cussion period open until June 1, 2010; separate discussions must be submitted for individual papers. This paper is part of the Journal of Bridge Engineering, Vol

27、. 15, No. 1, January 1, 2010. ©ASCE, ISSN 1084-0702/2010/1-73–80/$25.00.JOURNAL OF BRIDGE ENGINEERING © ASCE / JANUARY/FEBRUARY 2010 / 73Downloaded 09 Mar 2012 to 58.20.15.131. Redistribution subject to ASCE li

28、cense or copyright. Visit http://www.ascelibrary.orgRubber behavior is represented by a constitutive model based on the theory of hyperelasticity. In ABAQUS—theory manual version 6.6 ?2006?, the strain-energy density fun

29、ction proposed by Yeoh ?1993? is chosen. This model was used in the earlier study by Hamzeh et al. ?1998? as well. The Yeoh strain-energy density function is written in terms of the first invariant, I1, of the Green defo

30、rmation tensorW = C10?I1 ? 3? + C20?I1 ? 3?2 + C30?I1 ? 3?3 ?1?C10, C20, and C30 being material constants. The following values of these constants are used:C10 = 0.31384 MPa ?45.51864 psi?C20 = 0.021317 MPa ?3.09177 psi?

31、C30 = 0.00069279 MPa ?0.10048 psi? ?2?These values are obtained by scaling available test results for a carbon-black-filled rubber ?Hamzeh et al. 1995?. The scaling is such that the model exhibits a secant modulus in sim

32、ple shear, G, at 50% strain, equal to 0.6895 MPa ?100 psi?. Fig. 4 shows a graph of the simple-shear stress-strain curve for the rubber, as represented by the Yeoh model with the above parameter values. The steel is assu

33、med to be an elastoplastic material with Young’s modulus of 200 GPa ?2.9?107 psi?, Poisson’s ratio equal to 0.29, uniaxial yield stress of 276 MPa ?4.0?104 psi?, and tangent modulus beyond initial yielding of 1 GPa ?1.45

34、?105 psi?. The frictional contact between the pad and the rigid blocks at top and bottom is taken into account using the penalty formula- tion available in ABAQUS—theory manual version 6.6 ?2006?. This is a regularized r

35、epresentation of Coulomb friction with an allowable “elastic slip.” For relative displacements smaller than the elastic slip, it is assumed that “sticking” behavior occurs at the pad-girder, pad-pier, or pad-abutment int

36、erfaces. On the other hand, if the elastic slip is exceeded, “slipping” behavior is obtained at shear traction equal to the friction coefficient, ?, multiplied by the normal ?compressive? traction. In the present study,

37、we have set the elastic slip at 0.00254 mm ?10?4 in.? and ?=0.30. The steel-reinforced bearing is subjected to a sequence of two load steps. In Step 1 ?Fig. 5?, the pad is subjected to compression in the direction throug

38、h the thickness with the average stress, ?avg, set at ?3,447 kPa ??avg=?500 psi?. This level of compres- sion is the same as the one considered by Hamzeh et al. ?1998? in two-dimensional computations. In Step 2 ?Fig. 6?,

39、 the pad is sheared in various lateral direc- tions in the amount of one-half of the total rubber thickness ??s=hrt/2=22.225 mm=0.875 in.?. Seven shear directions are considered ?Fig. 7?: bridge longitudinal ?parallel to

40、 the z axis?, 15, 30, 45, 60, 75° with respect to the z axis, and bridge transverse ?90° with respect to the longitudinal axis?.Fig. 3. ?a? Mesh used in the computations ?shown: compressed rect- angular bearing

41、?; ?b? compressed rectangular bearing ?cross section? sheared in the longitudinal ?“traffic”? direction; and ?c? compressed rectangular bearing ?cross section? sheared in the transverse directionFig. 4. Simple shear: str

42、ess-strain curveFig. 5. Step 1—compressionFig. 6. Step 2—50% shearJOURNAL OF BRIDGE ENGINEERING © ASCE / JANUARY/FEBRUARY 2010 / 75Downloaded 09 Mar 2012 to 58.20.15.131. Redistribution subject to ASCE license or co